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        <h2 id="说明-2022-05-05"><a class="markdownIt-Anchor" href="#说明-2022-05-05"></a> 说明 - 2022-05-05</h2>
<p>本篇博客为本人原创, 原发布于CSDN, 在搭建个人博客后使用爬虫批量爬取并挂到个人博客, 出于一些技术原因博客未能完全还原到初始版本(而且我懒得修改), 在观看体验上会有一些瑕疵 ,若有需求会发布重制版总结性新博客。发布时间统一定为1111年11月11日。钦此。</p>
<h2 id="p4219-bjoi2014大融合"><a class="markdownIt-Anchor" href="#p4219-bjoi2014大融合"></a> P4219 [BJOI2014]大融合</h2>
<figure class="highlight cpp"><table><tr><td class="gutter"><pre><span class="line">1</span><br><span class="line">2</span><br><span class="line">3</span><br><span class="line">4</span><br><span class="line">5</span><br><span class="line">6</span><br><span class="line">7</span><br><span class="line">8</span><br><span class="line">9</span><br><span class="line">10</span><br><span class="line">11</span><br><span class="line">12</span><br><span class="line">13</span><br><span class="line">14</span><br><span class="line">15</span><br><span class="line">16</span><br><span class="line">17</span><br><span class="line">18</span><br><span class="line">19</span><br><span class="line">20</span><br><span class="line">21</span><br><span class="line">22</span><br><span class="line">23</span><br><span class="line">24</span><br><span class="line">25</span><br><span class="line">26</span><br><span class="line">27</span><br><span class="line">28</span><br><span class="line">29</span><br><span 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class="line">92</span><br><span class="line">93</span><br><span class="line">94</span><br><span class="line">95</span><br><span class="line">96</span><br><span class="line">97</span><br><span class="line">98</span><br><span class="line">99</span><br><span class="line">100</span><br><span class="line">101</span><br><span class="line">102</span><br></pre></td><td class="code"><pre><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;cstdio&gt;</span></span></span><br><span class="line"><span class="meta">#<span class="keyword">include</span> <span class="string">&lt;algorithm&gt;</span></span></span><br><span class="line"><span class="type">int</span> n, m, op, a, b, x , y;</span><br><span class="line"><span class="type">const</span> <span class="type">int</span> N = <span class="number">3e5</span>+<span class="number">4</span>;</span><br><span class="line"><span class="type">int</span> top, sdk[N], son[N][<span class="number">2</span>], fa[N],rev[N], sxor[N], sxor2[N];</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">pushup</span><span class="params">(<span class="type">int</span> x)</span></span>&#123;</span><br><span class="line">    sxor[x] = sxor[son[x][<span class="number">0</span>]] + sxor[son[x][<span class="number">1</span>]] + sxor2[x] + <span class="number">1</span>;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">hpushdown</span><span class="params">(<span class="type">int</span> x)</span></span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(rev[x])&#123;</span><br><span class="line">        rev[son[x][<span class="number">0</span>]] ^= <span class="number">1</span>;</span><br><span class="line">        rev[son[x][<span class="number">1</span>]] ^= <span class="number">1</span>;</span><br><span class="line">        rev[x] ^= <span class="number">1</span>;</span><br><span class="line">        std::<span class="built_in">swap</span>(son[x][<span class="number">0</span>], son[x][<span class="number">1</span>]);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">bool</span> <span class="title">isroot</span><span class="params">(<span class="type">int</span> x)</span></span>&#123;</span><br><span class="line">    <span class="keyword">return</span> son[fa[x]][<span class="number">0</span>] != x &amp;&amp; son[fa[x]][<span class="number">1</span>] != x;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="keyword">inline</span> <span class="type">void</span> <span class="title">pushdown</span><span class="params">(<span class="type">int</span> x)</span></span>&#123;</span><br><span class="line">    <span class="keyword">if</span>(!<span class="built_in">isroot</span>(x)) <span class="built_in">pushdown</span>(fa[x]);</span><br><span class="line">    <span class="built_in">hpushdown</span>(x);</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">rotate</span><span class="params">(<span class="type">int</span> x)</span></span>&#123;</span><br><span class="line">    <span class="type">int</span> y = fa[x], z = fa[y];</span><br><span class="line">    <span class="type">int</span> z2y = son[z][<span class="number">1</span>] == y, y2x = son[y][<span class="number">1</span>] == x;</span><br><span class="line">    <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y)) son[z][z2y] = x;</span><br><span class="line">    fa[x] = z, fa[y] = x, fa[son[x][y2x ^ <span class="number">1</span>]] = y;</span><br><span class="line">    son[y][y2x] = son[x][y2x ^ <span class="number">1</span>], son[x][y2x ^ <span class="number">1</span>] = y;</span><br><span class="line">    <span class="built_in">pushup</span>(y); <span class="built_in">pushup</span>(x);</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">splay</span><span class="params">(<span class="type">int</span> x)</span></span>&#123;</span><br><span class="line">    top = <span class="number">0</span>; sdk[++top] = x;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=x; !<span class="built_in">isroot</span>(i); i = fa[i]) sdk[++top] = fa[i];</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> i=top; i; i--) <span class="built_in">pushdown</span>(sdk[i]);</span><br><span class="line">    <span class="keyword">while</span>(!<span class="built_in">isroot</span>(x))&#123;</span><br><span class="line">        <span class="type">int</span> y = fa[x], z = fa[y];</span><br><span class="line">        <span class="keyword">if</span>(!<span class="built_in">isroot</span>(y))&#123;</span><br><span class="line">            <span class="keyword">if</span>((son[y][<span class="number">0</span>] == x) ^ (son[z][<span class="number">0</span>] == y)) <span class="built_in">rotate</span>(x);</span><br><span class="line">            <span class="keyword">else</span> <span class="built_in">rotate</span>(y);</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="built_in">rotate</span>(x);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">access</span><span class="params">(<span class="type">int</span> x)</span></span>&#123;</span><br><span class="line">    <span class="keyword">for</span>(<span class="type">int</span> t = <span class="number">0</span>; x; t = x, x = fa[x])&#123;</span><br><span class="line">        <span class="built_in">splay</span>(x);</span><br><span class="line">        sxor2[x] += sxor[son[x][<span class="number">1</span>]] - sxor[t];</span><br><span class="line">        son[x][<span class="number">1</span>] = t;</span><br><span class="line">        <span class="built_in">pushup</span>(x);</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">makeroot</span><span class="params">(<span class="type">int</span> x)</span></span>&#123;</span><br><span class="line">    <span class="built_in">access</span>(x); <span class="built_in">splay</span>(x); rev[x] ^= <span class="number">1</span>;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">find</span><span class="params">(<span class="type">int</span> x)</span></span>&#123;</span><br><span class="line">    <span class="built_in">access</span>(x); <span class="built_in">splay</span>(x);</span><br><span class="line">    <span class="keyword">while</span>(son[x][<span class="number">0</span>]) x = son[x][<span class="number">0</span>];</span><br><span class="line">    <span class="keyword">return</span> x;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">split</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> y)</span></span>&#123;</span><br><span class="line">    <span class="built_in">makeroot</span>(x); <span class="built_in">access</span>(y); <span class="built_in">splay</span>(y);</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">cut</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> y)</span></span>&#123;</span><br><span class="line">    <span class="built_in">split</span>(x, y);</span><br><span class="line">    <span class="keyword">if</span>(son[y][<span class="number">0</span>] == x &amp;&amp; son[x][<span class="number">1</span>] == <span class="number">0</span>)&#123;</span><br><span class="line">        son[y][<span class="number">0</span>] = <span class="number">0</span>; </span><br><span class="line">        fa[x] = <span class="number">0</span>;</span><br><span class="line">    &#125;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="type">void</span> <span class="title">link</span><span class="params">(<span class="type">int</span> x, <span class="type">int</span> y)</span></span>&#123;</span><br><span class="line">    <span class="built_in">makeroot</span>(x);</span><br><span class="line">    fa[x] = y;</span><br><span class="line">&#125;</span><br><span class="line"><span class="function"><span class="type">int</span> <span class="title">main</span><span class="params">()</span></span>&#123;</span><br><span class="line">    <span class="built_in">scanf</span>(<span class="string">&quot;%d%d&quot;</span>,&amp;n,&amp;m);</span><br><span class="line">    <span class="keyword">while</span>(m--)&#123;</span><br><span class="line">        <span class="built_in">scanf</span>(<span class="string">&quot;%*c%c%d%d&quot;</span>,&amp;op,&amp;x,&amp;y);</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">&#x27;A&#x27;</span>)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="built_in">makeroot</span>(x);</span><br><span class="line">            <span class="built_in">makeroot</span>(y);</span><br><span class="line">            fa[x]=y;</span><br><span class="line">            sxor2[y]+=sxor[x];</span><br><span class="line">        &#125;</span><br><span class="line">        <span class="keyword">if</span>(op==<span class="string">&#x27;Q&#x27;</span>)</span><br><span class="line">        &#123;</span><br><span class="line">            <span class="built_in">makeroot</span>(x); <span class="built_in">access</span>(y); <span class="built_in">splay</span>(y);</span><br><span class="line">            son[y][<span class="number">0</span>] = fa[x] = <span class="number">0</span>;</span><br><span class="line">            <span class="built_in">pushup</span>(x);</span><br><span class="line">            <span class="built_in">makeroot</span>(x); </span><br><span class="line">            <span class="built_in">makeroot</span>(y);</span><br><span class="line">            <span class="built_in">printf</span>(<span class="string">&quot;%lld\n&quot;</span>,(<span class="type">long</span> <span class="type">long</span>)(sxor[x]*sxor[y]));</span><br><span class="line">            <span class="built_in">makeroot</span>(x);</span><br><span class="line">            <span class="built_in">makeroot</span>(y);</span><br><span class="line">            fa[x]=y;</span><br><span class="line">            sxor2[y]+=sxor[x];</span><br><span class="line">        &#125;</span><br><span class="line">    &#125;</span><br><span class="line"></span><br><span class="line">    <span class="keyword">return</span> <span class="number">0</span>;</span><br><span class="line">&#125;</span><br></pre></td></tr></table></figure>

      
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